Solving a singular DAE model of unconfined detonation

We consider a simplified model of an unconfined one-dimensional detonation problem, giving a brief survey of the history of the problem and of its numerical solution. This problem with its mathematical features is typical of those solved commercially by ICI plc, and the specific values used for the chemical constants in the example are typical of those of interest. Unfortunately, not all obvious methods work well, because of the singular nature of the problem at the Chapman-Jouguet shock front. We concentrate on shooting methods for the detonation problem based on backward differentiation formula integrators, and present a new analysis which explains how these methods work. Finally, we outline some possibilities for further work, including discussing a more general detonation problem, previous solutions and potential future solution methods.